Applied Labor Project

This repository contains the code and exported outputs for the analysis of gender wage gaps before and after Covid.

Important distinction:

• simulated_data/ contains synthetic DADS-like data simulated for development, testing, and code validation.
• results/ contains the actual outputs obtained from the real DADS-Panel-like data used in the report. These are the results to use in the paper.

The real raw data are not stored in this repository. The scripts point to the simulated data.

Research Goal

The project studies whether changes after Covid are associated with changes in:

• the gender gap in hourly wages;
• the gender gap in firm premia;
• the sorting of women and men across firms;
• revealed firm values, access to job opportunities, and preferences over firms.

The Difference-in-Differences specifications are used as accounting tools to summarize changes in women-men gaps before and after Covid, not as strict causal estimates.

Main periods:

• full period: 2018-2022;
• pre-Covid: 2018-2019;
• post-Covid: 2021-2022;
• 2020 is excluded from the pre/post comparison.

Repository Structure

Applied-Labor/
  README.md
  src/
    simulate_dads_data.r
    descriptive_statistics.r
    model_estimation.r
    simulation_final.R
    simulation_full_yearly.r
    simulation_final.Rmd
    simulation_final.tex
  simulated_data/
    spell_year.parquet
    worker_year.parquet
    spell_month.parquet
    worker_month.parquet
    workers_pairs.parquet
    simulated_data_cache.rds
  results/
    tables/
      table1_labor_market_outcomes.tex
      table2_employment_transitions.tex
    figures/
      distribution_log_wage_gender_period.png
      distribution2_firm_premia_gender_period.png
      distribution_values_hat_gender_period.png
      compensating_differentials.png
    estimation/
      did_results_table.tex
      role_of_firms_gender_gap.tex
      gender_period_correlations.tex
      data_summary_by_year_gender.tex
      role_table_period_gender_wage.csv
      sorkin_lambda_estimates.csv
      sorkin_lambda_estimates_full_period.csv
      sorkin_preference_opportunity_by_period.csv
      sorkin_preference_opportunity_change.csv
      sorkin_preference_opportunity_table.tex

Data Structure

The project uses five DADS-like datasets.

spell_year

Stacked yearly job-spell data. One row is one worker-firm-year spell. A worker can have several rows in the same year if they changed employer during the year.

worker_year

Worker-year dominant-employer data. One row is one worker-year. The dominant employer is the firm associated with the highest annual net earnings in that worker-year.

spell_month

Monthly spell data derived from spell_year. One row is one employed worker-month. Yearly spells are expanded using debremu and finremu.

worker_month

Monthly worker panel derived from spell_month. One row is one worker-month. It includes employment and non-employment months until the worker's last observed month.

workers_pairs

Monthly transition data derived from worker_month. One row is one worker and one pair of consecutive months. It identifies:

• EE: employment-to-employment transition with firm change;
• E to NE: employment-to-non-employment transition;
• NE to E: non-employment-to-employment transition.

Scripts

src/simulate_dads_data.r

Creates synthetic DADS-like data for 20,000 workers and 1,000 firms over 2018-2022. The script exports the five parquet files in simulated_data/.

This script is useful for testing the full workflow without access to the real confidential data.

Run:

Rscript src/simulate_dads_data.r

src/descriptive_statistics.r

Creates descriptive tables and a descriptive wage-trends figure.

When run locally, the script uses the synthetic files in simulated_data/. However, the current tables stored in results/tables/ are the real-data versions used in the report.

Main outputs:

• results/tables/table1_labor_market_outcomes.tex;
• results/tables/table2_employment_transitions.tex;
• a parallel-trends-style wage figure when the script is run in the local workflow.

Definitions:

• Table 1 is computed from spell_year; outcomes are spell-level statistics.
• Table 2 is computed from the monthly panel reconstructed from spell_year.
• Transition rates are worker-level incidence rates: a worker is counted once if the transition occurs at least once in the period.
• The N workers row counts workers followed at the beginning of the corresponding period, whether or not they have an employment spell in that period.
• Average NE duration is the average total number of non-employment months among workers who have at least one non-employment month in the period.

Run:

Rscript src/descriptive_statistics.r

src/model_estimation.r

Main estimation script. In the repository version, inputs point to simulated_data/ and outputs point to results/, so the script can be run locally without external paths.

Near the top of the script:

data_dir <- file.path(project_dir, "simulated_data")
output_dir <- file.path(project_dir, "results", "estimation")
figure_dir <- file.path(project_dir, "results", "figures")

To run the same code on confidential real data, replace data_dir with the external folder containing the real parquet files. The report outputs stored in results/ are the real-data outputs.

The script estimates:

• AKM-style firm premia by gender and period;
• descriptive Difference-in-Differences regressions for log hourly wages and firm premia;
• Sorkin-style firm values and offer probabilities from mobility transitions;
• preference and opportunity decompositions;
• correlations between male and female firm values, firm premia, and compensating differentials;
• role-of-firms decomposition tables.

Run:

Rscript src/model_estimation.r

src/simulation_final.R and src/simulation_full_yearly.r

Older simulation and validation scripts used to develop and test the recovery of firm values and ranking methods before adapting the workflow to DADS-like files.

src/simulation_final.Rmd

Readable R Markdown version of the simulation exercise. The rendered output is src/simulation_final.tex.

Results Folder

The results/ folder is the folder to use for the report. It contains outputs from the real data, not merely simulated examples.

results/tables/

Contains the descriptive LaTeX tables:

• table1_labor_market_outcomes.tex: labor market outcomes and workforce composition by gender and period;
• table2_employment_transitions.tex: employment transitions and mobility by gender and period.

results/figures/

Contains report figures:

• distribution_log_wage_gender_period.png: distribution of log hourly wages by gender and period;
• distribution2_firm_premia_gender_period.png: distribution of AKM firm premia by gender and period;
• distribution_values_hat_gender_period.png: distribution of recovered firm values by gender and period;
• compensating_differentials.png: relationship between recovered firm values and AKM firm premia.

results/estimation/

Contains estimation tables and compact exports:

• did_results_table.tex: descriptive DiD regressions for wages and firm premia;
• role_of_firms_gender_gap.tex: main role-of-firms decomposition table;
• gender_period_correlations.tex: correlations between male and female firm values, firm premia, and compensating differentials;
• data_summary_by_year_gender.tex: annual summary statistics by gender;
• role_table_period_gender_wage.csv: mean wages by gender and period used in the role-of-firms decomposition;
• sorkin_lambda_estimates.csv: lambda estimates by gender for pre/post periods;
• sorkin_lambda_estimates_full_period.csv: lambda estimates by gender for the full period;
• sorkin_preference_opportunity_by_period.csv: preference/opportunity decomposition by gender and period;
• sorkin_preference_opportunity_change.csv: post-minus-pre change in that decomposition;
• sorkin_preference_opportunity_table.tex: LaTeX table for the preference/opportunity decomposition.

Methodological Notes

Descriptive Difference-in-Differences

The coefficient on Female x Post measures the post-Covid change in the women-men gap relative to the pre-Covid period, conditional on the included controls and fixed effects.

Adjusted specifications include worker and year fixed effects, sector fixed effects at the A38 level, occupation fixed effects at the PCS4 level, and time-varying controls when available:

• age, age squared, and age cubed;
• experience and experience squared;
• firm tenure and firm tenure squared;
• part-time status.

Because worker fixed effects absorb time-invariant worker characteristics, the main coefficient of interest is the interaction Female x Post.

AKM Firm Premia

AKM firm premia are estimated separately by gender and period. The firm premia are normalized so that their weighted mean is zero within each gender-period cell:

sum_j s_jgt psi_jgt = 0

No specific firm is chosen as the zero-premium reference firm. This normalization fixes only the level of the firm effects and does not affect differences across firms or changes in gender gaps across periods.

The AKM residualization includes worker/job controls and year effects. Sector and occupation fixed effects are excluded from the AKM firm-premium estimation because they are closely related to firm affiliation and may absorb part of the firm component.

Sorkin-Style Firm Values

The Sorkin-style part uses worker mobility transitions to recover firm values and offer probabilities. The algorithm focuses on firms connected through observed mobility transitions, because firms without mobility links do not provide identifying variation for recovered firm values.

R Packages

Main packages:

• data.table;
• arrow;
• dplyr;
• tidyr;
• ggplot2;
• Matrix;
• igraph;
• fixest;
• modelsummary optional, used for LaTeX regression tables.

Install missing packages with:

install.packages(c(
  "data.table", "arrow", "dplyr", "tidyr", "ggplot2",
  "Matrix", "igraph", "fixest", "modelsummary"
))

Recommended Workflow

For local testing with simulated data:

Rscript src/simulate_dads_data.r
Rscript src/descriptive_statistics.r
Rscript src/estimation_update2.r

For the real data:

1. make sure the five parquet files exist in the external processed data folder;
2. update data_dir in src/model_estimation.r so that it points to the real processed data folder;
3. run:

Rscript src/model_estimation.r

Then copy or keep the relevant exported tables and figures in results/.

Report Notes

• Use results/ for the report outputs.
• Treat simulated_data/ as a development and testing input, not as the source of the final reported estimates.
• The parallel-trends figure is best presented as a descriptive appendix check, not as a formal validation of a causal DiD design.
• The DiD estimates should be described as conditional changes in gender gaps, not as causal effects of Covid.